Commuting Operators: Understanding How M1,M2 & M3 Work Together

[Raptor112]

Homework Statement

It is known that $M_1,M_2, M_3$ commute with each other but I don't see how the second line is achieved even though it says that it's using that $M_1$ and $M_2$ commute?

 

[TSny]

Note M₂(1+M₁) = M₂ + M₂M₁

How can you rewrite the right hand side using the fact that M₁ and M₂ commute?

 

[Raptor112]

Note M₂(1+M₁) = M₂ + M₂M₁

How can you rewrite the right hand side using the fact that M₁ and M₂ commute?

$M_2 + M_1M_2$

 

[TSny]

$M_2 + M_1M_2$

OK. Can you see something you can do with this expression that will help?

 

[Raptor112]

OK. Can you see something you can do with this expression that will help?

$(1 +M_1)M_2$ ?

 

[TSny]

Yes.